Question

The rationalising factor of 2( √2 + √3) is

a) ( √2 + √3) b) 2 √2 − √3) c) √2 − √3 d) 2( √2 + √3 )^2


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Answer 1

Step-by-step explanation:

ANSWER:-

Given:-

• rationalising factor of 2( √2 + √3)
• We need the rationalised answer in order to find the correct answer.

Concept:-

Rationalisation of numbers.

Let's Do!

Here, we need to find the suitable factor b uh which we can find the rationalised and simple answer.

So, we will try with all the options provided.

a) ( √2 + √3)

We know that Rationalisation occurs with different and opposite sides, cancelled.

b) 2 √2 − √3)

The signs is okay, but 2 is shared with one which will again give us a square root number, which is not needed.

d) 2( √2 + √3 )^2

On squaring the number, by the identity :-

$\rm{(a+b)^2 = a^2 + b^2 + 2ab}$

In which we will get the middle factor as square root term, so cancelled.

c) √2 − √3 ✔

Here we will apply the identity:

$\rm{(a+b)(a-b) = a^2 - b^2 }$

This will give us a rationalised term, and hence the required answer.

Answer 2

Qᴜᴇsᴛɪᴏɴ ɪs ɢɪᴠᴇɴ ʙᴇʟᴏᴡ -

➦ The rationalising factor of 2( √2 + √3 ) is

Option a ➨ ( √2 + √3 )

Option b ➨ 2 ( √2 − √3 )

Option c ➨ √2 − √3

Option d ➨ 2( √2 + √3 )²

Sᴏʟᴜᴛɪᴏɴ ɪs ɢɪᴠᴇɴ ʙᴇʟᴏᴡ -

Option c ➨ √2 − √3

Fᴜʟʟ sᴏʟᴜᴛɪᴏɴ -

Option c ➨ √2 − √3 is correct because in this we have to use the identity ( rationalising factor ) –

= (a + b)(a - b) = a² - b²

Option a ➨ ( √2 + √3 ) is wrong because in this none digit ( different and opposite sides ) is cancelled.

Option b ➨ 2 ( √2 − √3 ) is not correct because there are signs of square root and one is not needed to rationalising factor.

Option d ➨ 2( √2 + √3 )² is not correct because while using identity the solution isn't come and it's cancel wrongly.